Question

Precise offers People often use round prices as first offers in a negotiation. But would a more precise number suggest that the offer was more reasoned and informed? In an experiment, $238$adults played the role of a person selling a used car. Each adult received one of three initial offers: $\backslash (2000$, $\backslash )1865$(a precise under-offer), and $\backslash (2135$(a precise over-offer). After hearing the initial offer, each subject made a counter-offer. The difference in the initial offer and counter-offer was the largest in the group that received the $\backslash )2000$ offer. Describe how the researchers could have randomly assigned the subjects to the treatments

a. using slips of paper.

b. using technology.

c. using Table D.

Short answer

Part(a) Researchers could have randomly assigned to the treatments writing all the numbers seperately using slips of paper.

Part(b) Researchers can assign three treatments to different volunteers at random using technology.

Part(c) Researchers can assign this method to each participant separately.

Step-by-step solution

Part(a) Step 1 : Given information

We need to find how researchers can randomly assign the subjects to the treatments using slips of paper.

Part(a) Step 2 : Simplify

Write the digits 1, 2, and 3 on separate pieces of paper.

Treatment 1 : $\$2000$

Treatment 2 : $\$1865$

Treatment 3 : $\$2135$
Arrange the sheets on a table, numbers facing down.
Mix the sheets together until you can't tell which number belongs where on the table.
Choose one of the slips of paper and apply the treatment that corresponds to the number to the subject.
Continue until all of the subjects have been given a therapy.

Part(b) Step 1 : Given information

We need to find how researchers can randomly assign the subjects to the treatments using technology.

Part(b) Step 2 : Simplify

The researchers aim to know if people commonly utilise round prices as the first offer in a negotiation or not in this study.
As a result, the researchers might have used technology to randomly assign the participants to the therapies by;
The random number drawing approach can be used to perform random allocation using technology.
Draw a random number from uniform $(0,0.9)$and go with first pick if the number is between $0$and $0.3$.
Assign second choice if the number is within $0.3-0.6$, and third choice if the number is not within $0.3-0.6$.
Those three treatments can be assigned to different volunteers at random using this method.

Part(c) Step 1 : Given information

We need to find how researchers can randomly assign the subjects to the treatments using Table D.

Part(c) Step 2 : Simplify

The researchers aim to know if people commonly utilise round prices as the first offer in a negotiation or not in this study.
So, using technology, the researchers may have randomly assigned the participants to the therapies; Table D is unclear, but it could be a random number table.
Each of the three treatments can be assigned at random using a random number table.
Pick a one-digit number between $1$and $9$ at random.
Find the remaining by multiplying the number by three.
If the residual is $0$, select the third option; otherwise, use the reminder number option.
Apply this method to each participant separately.